What is the Least Common Multiple of 51504 and 51514?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 51504 and 51514 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 51504 and 51514, than apply into the LCM equation.

GCF(51504,51514) = 2
LCM(51504,51514) = ( 51504 × 51514) / 2
LCM(51504,51514) = 2653177056 / 2
LCM(51504,51514) = 1326588528

Least Common Multiple (LCM) of 51504 and 51514 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 51504 and 51514. First we will calculate the prime factors of 51504 and 51514.

Prime Factorization of 51504

Prime Factorization of 51514

Now multiplying the highest exponent prime factors to calculate the LCM of 51504 and 51514.

LCM(51504,51514) = 2⁴ × 3¹ × 29¹ × 37¹ × 43¹ × 599¹
LCM(51504,51514) = 1326588528